Hubble (the man) discovered in the 1920's that galaxies far away are redshifted, meaning that their light waves have been stretched. The further the galaxies tended to be the more redshifted their light. Red shift of light is the same basic Doppler affect as when you hear a car pass you by. The pitch of the sound waves drop. This redshift could be seen in all directions that he looked, and so from this he could tell that galaxies on the whole were getting farther and farther apart from one another. The universe is expanding which implies that the universe had a beginning when all things were all together.
This disturbed most at that time, because many felt that the universe was basically changeless. That the universe had a beginning disturbed many. One scientist who was against this beginning theory, called the theory in 1949, the "Big Bang" and the name stuck. So this unflattering name was given to this beginning of the universe theory, which has only gained more evidence in it's favor as time and science has progressed. The Big Bang theory is a theory based on observational evidence that the universe had a beginning.